{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73975d39",
   "metadata": {},
   "source": [
    "**<font size=4 color=#BB3D00 face=微软雅黑>下采样-混叠</font>**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2df9d3c1",
   "metadata": {},
   "source": [
    "<font size=3  face=微软雅黑>**※Matlab案例**</font> "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "409b9a38",
   "metadata": {},
   "source": [
    "网址：https://ww2.mathworks.cn/help/signal/ug/downsampling-aliasing.html   \n",
    "描述：本案例由2个示例构成：   \n",
    "- <font color=DarkOrChid>示例1：如何在对信号进行下采样时避免混叠</font>\n",
    "- <font color=DarkOrChid>示例2：哪种下采样时无混叠</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce23a0cd",
   "metadata": {},
   "source": [
    "<font size=3 face=微软雅黑>**※Python案例**</font> "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61f6d45f",
   "metadata": {},
   "source": [
    "针对以上案例，采用Python语言实现。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32d1fba2",
   "metadata": {},
   "source": [
    "- <font color=DarkOrChid>示例1：如何在对信号进行下采样时避免混叠</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2ef818a",
   "metadata": {},
   "source": [
    "此示例说明如何在对信号进行下采样时避免混叠。如果离散时间信号的基带频谱支持不限于宽度为 2π/M 弧度的区间，则以 M 为因子下采样会导致混叠。混叠是当信号频谱的多个副本重叠在一起时发生的失真。信号的基带频谱支持超出 2π/M 弧度越多，混叠越严重。以下示例演示了以 2 为因子下采样的信号中的混叠。信号的基带频谱支持超过了 π 弧度的宽度。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ff7c28a",
   "metadata": {},
   "source": [
    "创建一个基带频谱支持等于 3π/2 弧度的信号。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7c575348",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import signal\n",
    "from scipy import *\n",
    "\n",
    "f = [0,0.2500,0.5000,0.7500,1.0000]\n",
    "a = [1.00,0.6667,0.3333,0,0]\n",
    "nf=512\n",
    "b1=signal.firwin2(nf-1, f,a, nfreqs=None, window='hamming', nyq=None, antisymmetric=False, fs=None)\n",
    "[h1,h2]=fft.fftshift(signal.freqz(b1, 1, nf, whole=True, plot=None, fs=2*np.pi, include_nyquist=False))\n",
    "omg=np.linspace(-np.pi,np.pi-2*np.pi/nf,nf)\n",
    "fig = plt.figure(dpi=100,figsize=(8,6))\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax1.plot(omg/np.pi,abs(h1))\n",
    "plt.xlabel('$\\pi$ rad/sample')\n",
    "plt.ylabel('Magnitude')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "beedb621",
   "metadata": {},
   "source": [
    "以 2 为因子对信号下采样，并绘制下采样信号的频谱和原始信号的频谱。除频谱的幅值缩放之外，重叠频谱副本的叠合还会导致 ∣ω∣>π/2 的原始频谱失真。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "118b3e86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y1=b1[1::2] \n",
    "[h3,h4]=fft.fftshift(signal.freqz(y1, 1, nf, whole=True, plot=None, fs=2*np.pi, include_nyquist=False))\n",
    "fig = plt.figure(dpi=100,figsize=(8,6))\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax1.plot(omg/np.pi,abs(h1),label='Original')\n",
    "ax1.plot(omg/np.pi,abs(h3),label='Downsampled')\n",
    "plt.xlabel('$\\pi$ rad/sample')\n",
    "plt.ylabel('Magnitude')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbfa2f3d",
   "metadata": {},
   "source": [
    "将信号的基带频谱支持增加到 [−7π/8,7π/8] 并以 2 为因子对信号下采样。绘制原始频谱和下采样信号的频谱。频谱宽度的增加导致下采样信号频谱中更明显的混叠，因为有更多信号能量处在 [−π/2,π/2] 之外。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "381fa2ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f1= [0,0.2500, 0.5000, 0.7500, 7/8, 1.0000]\n",
    "a1= [1.00, 0.7143 ,0.4286, 0.1429, 0 ,0]\n",
    "nf=512\n",
    "b2=signal.firwin2(nf-1, f1,a1, nfreqs=None, window='hamming', nyq=None, antisymmetric=False, fs=None)\n",
    "[h1,h2]=fft.fftshift(signal.freqz(b2, 1, nf, whole=True, plot=None, fs=2*np.pi, include_nyquist=False))\n",
    "y2=b2[1::2] \n",
    "[h3,h4]=fft.fftshift(signal.freqz(y2, 1, nf, whole=True, plot=None, fs=2*np.pi, include_nyquist=False))\n",
    "omg=np.linspace(-np.pi,np.pi-2*np.pi/nf,nf)\n",
    "fig = plt.figure(dpi=100,figsize=(8,6))\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax1.plot(omg/np.pi,abs(h1),label='Original')\n",
    "ax1.plot(omg/np.pi,abs(h3),label='Downsampled')\n",
    "plt.xlabel('$\\pi$ rad/sample')\n",
    "plt.ylabel('Magnitude')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f846d24",
   "metadata": {},
   "source": [
    "- <font color=DarkOrChid>示例2：哪种下采样时无混叠</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aaaac6f5",
   "metadata": {},
   "source": [
    "最构造基带频谱支持仅限于 [−π/2,π/2] 的信号。以 2 为因子对信号下采样，并绘制原始信号的频谱和下采样信号的频谱。下采样信号是全频带信号。下采样信号的频谱是原始频谱的扩展和缩放版本，但频谱的形状得以保留，因为频谱副本不重叠。没有混叠。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "201e1e89",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f2= [0, 0.250 ,0.500 ,0.7500, 1]\n",
    "a2= [1.0000, 0.5000 ,0 ,0 ,0]\n",
    "nf=512\n",
    "b2=signal.firwin2(nf-1, f2,a2, nfreqs=None, window='hamming', nyq=None, antisymmetric=False, fs=None)\n",
    "[h1,h2]=fft.fftshift(signal.freqz(b2, 1, nf, whole=True, plot=None, fs=2*np.pi, include_nyquist=False))\n",
    "y2=b2[1::2] \n",
    "[h3,h4]=fft.fftshift(signal.freqz(y2, 1, nf, whole=True, plot=None, fs=2*np.pi, include_nyquist=False))\n",
    "omg=np.linspace(-np.pi,np.pi-2*np.pi/nf,nf)\n",
    "fig = plt.figure(dpi=100,figsize=(8,6))\n",
    "ax1 = fig.add_subplot(111)\n",
    "ax1.plot(omg/np.pi,abs(h1),label='Original')\n",
    "ax1.plot(omg/np.pi,abs(h3),label='Downsampled')\n",
    "plt.xlabel('$\\pi$ rad/sample')\n",
    "plt.ylabel('Magnitude')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8340724b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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